Negative resistance amplifiers



Dec. 25, 1956 w. P. MASON ET AL NEGATIVE RESISTANCE AMPLIFIERS Filed Aug. 1, 1952 FIG. 5

FIG.

mp. MASON w. SHOCKLEY A 7'TORNEY United States Patent NEGATIVERESISTANEE *A'MPIJFIERS TWarren -Mason, West Orange, and "William Shockley, Madison, "N.J., assignors to Bell Telephone Laboratories, Incorpm'ated, New "York, N. -Y., a cnrpcration 'of NewiYork z Application August 1, 1952, Serial No. 302,278

.4v Claims. (Cl. 179-171) of';-thewposvi-tive circuit resistance and thereby to secure -tone" desiralble cited or another. Negative resistance ele- :"rnents have be'enused in wave transmission circuits, for wexample, TOSCI'VB? as so called booster amplifiers ;.of the vtransmitted waves. The-amplification-or-other eitect .ris lgreatersthe moreinearly: the negative resistancecancels 'YtthCI'lPO'SitiVC'TeSlSt311C6,"b1ltlHS133Jb1ilty0I oscillation will -occur uthe negative resistanceabecomes equal to or greaterxthan the positiveresistance. It has been necessary. torforego-close balance ofnegative and positive reusistancesntoi allownmargin l fior inconstancy of eitherthe negative-resistance itself, -or the resistance of r the associated circuits. These latter variationsrrmay, incidently, be radical in such cases :as the opening and closing of telephone circuits in switching operations. This accounts in part 'tor the rare use of rthe simpler two-terminal or elemental negative, resistance elements and the more widespread use of the we'llknown tour terminal conventional vaouumtube amplifier, up. to the, present time.

IMore specific objects, then, are to allow a close 'balvance laetweeupos'itive and negative resistance, tolachieve a higher margin against instalibity, and to allow. easier tolerances on the positive and negative resistance elements.

"In -alternating current circuits there may he reactive components which restrict the benefit or amplification from negative resistance even when the reactive comvuponent iswunchanging, and ,aWEurtherwobjecti-s 510 overcome this restriction.

I stilleanotherrobjectwof this inventionwisto provide a simple, inexpensive electrical transducertwhich Iwill readily *pass alternating current inone direction but notwinwthe -other, and Which has a ibroad-tfrequency characteristic, -to :bet-usedin combination with sensitiveelectriccomponents such as negative resistance .elements.

'In accordance with the inventiomthe objects mentioned "and --others which will the developedaaretattained by associating passive non-reciprocal .tnansrnission networks with negative --resistance elements or other. sensitive electrical components in such manner that theeflects of impedance variationsin one part of the circuit are isolated tromthe other parts, 'and the unstabilizing effects are reduced.

.More specifically, thexinvention contemplates the :interposition between thenegative resistance 'elementand associated elements of -inconstant impedance, a nonrrecipmcal circuit-unit having xdireetionally asymmetric characteristicst uA teature 'of -theinvention lies in the use of la plurality' of' nega'tive resistanceelements:alternatedtwithnonreciprocal networks of the type noted.above,;to 'crea-teza sta ble hi'gh gain amplifier.

An radditionalteatureof theinvention lies. in'the comhination of. an unstable .or variable electrical impedance with a non-reciprocal circuit unit having directionally asymmetric characteristics which is simple, passive, stable and has a broad frequency response.

The nature of the present invention and various objects, features, and advantages in addition to those pointed out above will appear more fully "from the following descript-ion of the embodiments :of the invention which are il-lustratedin the drawings. I

In the drawings: Y

Fig. -1 is a vol-tage-cur-rent pl'ot of a negative resistance element; I

Fig. 2 is the circuit of a negative resistance unit;

Figs. 3, 4 and '5 show known circuits employing negative resistances in series, shunt and combination arrangements, respectively;

Fig. 6 represents a Hall effect directionally asymmetric element or gyrator;

"Fig. 7 illustrates a nonreciprocal or unidirectional circuit employing aHal l effect fgyrator;

Fig. '8 depicts the use of a non-reciprocal circuit separating .two series negative impedances;

Fig. 9 shows two non-reciprocal circuital units effectively isolating a negative resistance; and

Figs. 10 and 11 show plural stage amplifiers employing series and shunt type negative resistances, respectively.

Prior to entering on a detailed discussion of the drawings and a mathematical analysis of the factors involved, v

a 'cursory'statement ofthe electrical elements and circuital units involvedin this application will be set forth. The two important elements involved in "this application are first,*negative resistance elements and, secondly, nonreciprocal transducergwhich l have difierent transmission charac-teristicstor the two directions of transmission. The -vo1tage-currentplot of a representative negative resistance element is shown in Fig. 1. Note that witha biasing current of Io, Whendhe .current increases, the voltage .drops, andvice versa. For alternating currents, the device "biasedatthis point-may thus he seen to have -a negative resistance. Partially because of their critical biasedoperating-conditions, many of the simpler, or elementalynegative resistance elements .are quite sensitive, 45 t and this tendency toward :instahility has limited their usefiulness.

A tour-terminal electrical network is said to satisfy the R-eciprocityTheorem if fan electrornotivel-torce E applied between .two terminals produces a current lat twowother terminals, andcthe same voltage E :a-ctinglat ;th'e secondv point in the circuit .will produce the same cur-- :rent I.atsthelfirstpoin-t. As set forth by=E. M.-McMi-llan in :his lart-icle,vz pa-ges 344-through 347 of volume-l8 'of the J ournal of the Acoustical Society of America'('1946) .a iour terminal .linearpassive "system satisfies-the reciprocity theorem lit the :transfer impedances in-cach ,di-

rection are equal. Thus, where. the:current-voltage relationships ton-each side of 1a networkare given lay the expressions:

workis said' to :be reciprocal. Most passive circuit net-- works 'dosatisty the Reciprocity Theorem, and are reciprocal. In theapresent application, .however, we-will Another non-reciprocal transducer, to which repeated 4 reference will be made in the balance of this application, is the gyrator, a transducer in which the phase shifts differ by 180 degrees for the two directions of propagation. When this type of directional phase shifting transducer is paralleled by normal reciprocal elements having the same phase shift for both directions of transmission, the current flow in the in-phase direction is enhanced while that in the out-of-phase direction is canceled, either partially or completely. This type of unit which transmits or conducts alternating current signals with less loss in signal amplitude for one direction than for the other will be termed a directional transducer. It further appears that my alternating negative resistance elements and directional transducers of this type, the sensitive negative resistances are effectively stabilized through isolation, and

will thus be of much greater utility than they have been up to the present time.

Proceeding now to a more detailed consideration and analysis of the invention as shown in the drawings, Fig. 1 is a plot of the voltage-current characteristic of a representative negative resistance element. In particular, it is that of the high speed thermistor disclosed in application Serial No. 199,868, of J. A. Becker and M. C. Waltz, filed December 8, 1950, now Patent 2,740,940 granted April 3, 1956. With the thermistor biased at a current of In amperes, it will be noted that a slight increase of current will result in a decrease of voltage across the thermistor instead of the normal increased voltage drop found in positive resistance elements. As is developed in more detail in the above-noted application of Becker and Waltz, the particular high speed thermistor plotted in Fig. 1 exhibits this negative resistance characteristic up to about 100 kilocycles.

Another negative resistance element is the gas diode. At wave guide frequencies negative resistance elements of the type disclosed or referred to in Patent No. 2,308,523 to F. B. Llewellyn, and which issued January 19, 1943, would be suitable. For very high frequency work, however, the negative resistance characteristic resulting from transit time effects across a thin layer of a semiconductor such as germanium may also be employed. This latter type of negative resistance element is disclosed in Patent No. 2,569,347, which issued to W. Shockley on September 25, 1951. E. W. Harold in an article in volume 23, No. 10, page 1201 of the Proceedings of the I. R. E. mentions many other devices for obtaining negative resistance which could also be used in circuits in accordance with the present invention.

In Fig. 2, the components of a negative resistance element corresponding to the plot of Fig. 1 are shown. The biasing current for the thermistor T is supplied by the direct current voltage source EB through the resistance RB. The bypass condenser C confines the thermistor biasing current to the local circuit. In the drawings, the symbol for a regular resistance and the designation RN will be used to indicate negative resistance elements of any of the types mentioned in the preceding paragraphs.

The simplest methods for obtaining gain with negative resistance elements are shown in the series and shunt arrangements of Figs. 3 and 4, respectively. Negative resistance elements are classified as series stable or shunt stable and have to be used respectively in the series or shunt arrangements such as shown in Figs. 3 and 4.

. For the series arrangement the current amplification obtained by introducing a negative resistance RN1 between the signal source with its resistance R1 and the load resistance R2, which are designated terminating resistances, is given by where i1 is the current without, and i'1 is the current with the negative resistance RN in the circuit. Hence, if RN nearly annuls the sum of R1 and R2, a very high gain is obtained. In the shunt case of Fig. 4 where i'z and it: are the currents with and without negative resistance, the gain is given by Hence, if Ru is slightly larger in magnitude than R1R2/(R1-I-R2), a stable gain is also obtained.

However, gain obtained this way depends to a large extent on the stability properties of the negative resistance elements and also on the load. For example, to obtain a stable gain of 60 db which corresponds to a ratio of iz/iz of 1000 to 1 then it may be seen from Equation 1 that RN must equal .999(R1+R2) and may not increase by as much as .1 percent. Any small change in Rm or (R1+R2) such as would make the total circuital resistance negative will cause the device to sing or oscillate, and a slightly lesser change in this direction would change the gain by large factors. The same situation is true for any combination of negative and positive impedance elements. For example considering the T network of negative resistance elements between two equal terminating resistances R1 as shown in Fig. 5, it is readily shown that the gain obtained by inserting them between the two resistances R1 is A large stable gain is obtained when R1v |R and RN4 IR1RN3I- If a gain of 60 db is to be obtained, the most stable arrangements of negative resistance elements will be when R1v =.967 R and 2Rzv is equal to 1.033 (R R1v Under these conditions the gain is equal to and the sum of the negative resistance terms of Equation 4 may not exceed 0.001 or 0.1 percent of the abovenoted values, and no gain in stability is obtained by dividing the amplifying process between several negative resistance elements. For purposes of later comparison, it will further be noted that each of two series connected equal negative resistances may not increase by more than 0.2 percent for a stable GO-decibel gain.

Bypassing Figs. 6 and 7 for the moment, Figs. 8 through 11 illustrate circuits designed in accordance with the invention. In these arrangements, the instability which has plagued circuits using simple negative resistances has been overcome. Negative resistances are cascaded into high gain stable amplifiers, variations of terminating impedances have a negligible effect on the sensitive negative resistances, and many other advantageous results are secured. The means of securing these remarkable ends is the association with the negative resistances of the passive directional transducers mentioned above. As shown in Figs. 8 through 11, these inexpensive, unilaterally conducting four-terminal networks have been found to effectively isolate negative resistances from undesired unstabilizing effects.

One method for obtaining such non-reciprocal networks is the Hall effect plate: or gyrator which is described in P. Mas'ons application-SerialNo. 219,342 now Patent 2,649,574, filed April5, 1951, now Patent 2,649,574, granted August lS, 1953. Itmay readily be shown that the gyrator alone, if symmetrical, can be represented by equations of the type- Ez Rzth-l-Rniz where R21'=R12 and that these values of resistance are independent ofthe frequency up to cycles or higher. With a permanent magnet giving a field of 17,500 Gauss, and using a germanium Hall element .220 inch square and .045 inch thick, values of Ri1=340 ohms and R21=78 ohms were obtained. The. actualvalues of R11 depend on the shape and resistivity of the material but the ratio R11/R21 is fixed by the nature of the material and the value of the magnetic field. Fig. 6 shows the voltages E2 in terms of i1 and in, we find the following expressions for the overall unit shown in Fig. 7:

That is, there is a coupling resistance R21 in one direction but no coupling resistance R'12 in the other. The value of the shunt resistance 2Rs that causes this balance is With this value of shunt resistance the transducer of Fig. 7 (including the Hall effect gyrator and the shunt resistances) has a transfer impedance which includes.

equal reciprocal and non-reciprocal components. For one direction of transmission of alternating current signals, the reciprocal component and the non-reciprocal, or gyrator, component are additive. For the opposite direction of transmission, however, the sign of the gyrator.

component is reversed, and it substantially cancels out the reciprocal component of the transfer impedance.

The insertion loss caused by inserting the balanced gyrator between two terminating resistances equal to the self resistance R11 is given by the Equation 9:

9 i 21%, 596 0 186 or 14.6 db with the values of R11=340 ohms; R21=R12=78 ohms. This represents a gain of 4.3 db over the gyrator alone due to the additional transmission through the shuntingresistance Rs. For the other direction R'21 is replaced by R'iz but since this is zero in Equation 7 the loss in the back direction is infinite; actually about 60 db difference occurs between the transmission in the two directions, with the circuital arrangement as set forth above.

In addition to Hall eifect plates, directional transducers may be made of other elements. In the McMillan article cited above, for example, a mechanically coupled crystal and magnetic transducer unit is shown to have gyrator properties over a. restricted band. of frequencies. Other alternatives aresuggested in C..L..Hogans article on The microwave gyrator, pages 1-31 of theiBell System Technical Journal, volumeXXXLJanuary 1952. This article also discusses at page 25 a particular type of' directional transducer for use at microwave frequencies which employs a directional plane of polarization shifting-element of the Faraday'elfect type. Inthis connection, it is interesting to note that a polarizing force, which in several of the present examples is a magnetic field, acting asymmetrically on an element in the transmission path, constitutes the physical basis for the unilateral conducting properties of these directional transducers of the Faraday and Hall eifect types. The possibility of making certain other specific unidirectionally conducting transducers is set forthin the McMillan article and. also W. P. Mason at pages 344-356 of his book entitled Electromechanical Transducers and Wave Filters, 2nd edition, D. Van Nostrand Co., Inc., 1948. It "may be noted that the Me- Millan balanced gyrator arrangement is only precisely balanced and unidirectional at a single frequency, al-

.though it will have useful non-reciprocal properties over a broader range. Similarly, the non-reciprocal qualities of the Hall effect gyrator plus resistances would be useful even if impedance deviations prevented anexact balance. The term directional transducer will thus include a gyrator and the additional elements or modified structure required to make it transmit better in one direction than the other. This term will include balanced gyrators, which are substantially unilaterally conducting transducers including a gyrator. The. symbol for directional transducers of any of the types noted above will be a box with a symbol 1;; RI21(ZT1+ZT2) 2 '11+ r -RN ][R' +Z R If the terminating impedances are resistances and the negative resistances RN and RN, are adjusted till the sum and similarly RI11+RT2-RN6=AR2 (12) the transmission loss (which will be a gain if ARi and ARz are small) becomes and the gain introduced by each negative resistance is independent of. the other. Hence the gains can be cascaded without introducing any more instability than occurs for each negative resistance by itself.

In particular, if a gain of 60 decibels is divided between the two stages of amplification including RN5 and Ru then neglecting gyrator losses, each negative resistwhere Ru and R21 are the constants of the first gyrator, Ru and R21, those of the second gyrator and ZT and Zr, the terminating impedances. Hence by making the sum of small, a large gain can be obtained irrespective of the values or variations of the terminal impedances Z'r and ZTT Hence the negative resistance is effectively isolated from the effects of the terminations. By introducing more gyrators with negative resistances between them as shown in Fig. 10, gain can be cascaded without regard to the terminations with the stability depending only on sums of the type shown by Equation 15.

Similar results can be obtained with cascaded shunt type negative resistances as shown in Fig. 11. An equation similar to (14) for the gain of introducing a shunt negative resistance between two balanced gyrators is R21 R21 T a The foregoing is an analysis of the value of applicants contribution as applied to some of the systems illustrated in the drawings. Summarizing the more important ad vantages of this type of circuit, as; developed above, it appears that terminal impedance variations can be isolated, negative resistances can be used as amplifiers even when the terminal impedance is highly reactive, and sensitive negative resistances may be cascaded without adverse interaction from impedance changes in other stages. The usefulness of the invention over a broad frequency band extending into microwave frequencies is also considered worthy of reiteration.

It is to be understood that the above-described arrangements are illustrative of the application of the principles of the invention and that numerous other arrangements may be devised by those skilled in the art without departing from the spirit and scope of the invention.

A related application of William Shockley, Serial Number 303,642 was filed concurrently with the present application. An application of C. L. Semmelman, Serial Number 307,263, filed August 30, 1952, also deals with related subject matter.

What is claimed is:

1. In an alternating current signal circuit, a two terminal negative resistance, means for coupling said negative resistance in linear amplifying relationship with said alternating current signal circuit, and a directional transducer interposed in said signal circuit, said transducer including a gyrator and a reciprocal signal transmission path connected to said signal circuit in such bridging relation- RN is slightly larger than 17 ship with said gyrator as to increase the amplitude of signals transmitted through said signal circuit in one direction and substantially cancel signals transmitted in the other direction, the reciprocal component of the transfer impedance of said transducer being substantially equal to the gyrator component of the transfer impedance.

2. In an alternating current signal circuit, a plurality of directional transducer devices each including a gyrator interposed in said signal circuit and a reciprocal signal transmission path connected to said signal circuit in such bridging relationship with said gyrator as to increase the amplitude of signals transmitted through said signal circuit in one direction and substantially cancel signals transmitted in the other direction, the reciprocal component of the transfer impedance of said transducer being substantially equal to the gyrator component of the transfer impedance, a plurality of two terminal negative resistances, and means for coupling said negative resistances in linear amplifying relationship with said alternating current signal circuit at points which are separated by said directional transducer devices.

3. In an alternating current signal circuit, a two terminal negative resistance, means for coupling said negative resistance in linear amplifying relationship with said alternating current signal circuit, and a directional transducer device interposed in said signal circuit, said directional transducer including a gyrator and a reciprocal signal transmission path connected to said signal circuit in such bridging relationship with said gyrator as to increase the amplitude of signals transmitted through said signal circuit in one direction and reduce the amplitude of signals transmitted in the other direction, the reciprocal component of the transfer impedance of said transducer being of the same order of magnitude as the gyrator component of the transfer impedance and having such a value as to prevent oscillations in said signal circuit.

4. In an alternating current signal circuit, a two terminal negative resistance, means for coupling said negative resistance in linear amplifying relationship with said alternating current signal circuit, and a directional transducer interposed in said signal circuit, said transducer including a Hall effect gyrator unit having two input terminals and two output terminals connected in said alternating current signal circuit, a first shunt resistance connected between one input terminal and one output terminal of said gyrator unit, and a second shunt resistance connected between the other input terminal and the other output terminal of said gyrator unit, each said shunt resistance having the following value:

R1i -l- 21 2R2.

where R11 is the resistance between two input or two output terminals, and where R21 is the transfer resistance between the input and output terminals of the gyrator unit.

References Cited in the file of this patent UNITED STATES PATENTS 2,553,490 Wallace May 15, 1951 2,585,571 Mohr Feb. 12, 1952 2,647,239 Tellegen July 28, 1953 2,649,574 Mason Aug. 18, 1953 2,697,759 Tellegen Dec. 21, 1954 OTHER REFERENCES The Gyrator, Tellegen, Phillips Research Report 3, PP. 81-l0l, April 1948 (see especially p. 88). i 

